we may use BODMAS in answering this question you divide 18 by 6 and your answer will be 3 you then add 5 to the 3 to obtain your answer which is 8
Estimate and then compute the product check that your answer is reasonable
759 x 68
The estimate of the product is reasonable
How to estimate and then compute the product check that your answer is reasonable?The product expression is given as
759 x 68
As an estimate, we have
759 - 760
68 = 70
So, we have:
759 x 68 = 760 * 70
Evaluate the product
759 x 68 = 53200
For the actual product, we have
759 x 68 = 51612
The estimate and the actual product both approximate to 50000
Hence, the estimate of the product is reasonable
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Determine if each statement is true or false. Justify your answer.
log₄7- log ₄3= log₄4
The given logarithmic expression statement is false. Because log₄7- log ₄3 = log₄(7/3).
The logarithm is exponentiation's opposite function in mathematics. This means that the exponent to which a fixed number, base b, must be raised in order to produce a given number x, is represented by the logarithm of that number.
Based on the logarithm base, the logarithmic functions are broadly divided into two types. There are common and natural logarithms. Common logarithms are based on the number 10, while natural logarithms are based on the base "e." The power to which a number must be raised in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents).
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What are some reasons you should be intentional about saving money? in other words,
Answer:
Step-by-step explanation:
The reason why you should save money because if you spend all of your money you won't able to take care of yourself, your house, or have nothing to do
What is the solution of √4 x+1 -5=0 ?
The solution is 6
Rewriting the given equation
√(4x + 1) - 5 = 0
Now, taking square of the equation to find the solution of equation -
(√(4x + 1))² = 5²
On squaring both sides we get the equation -
4x + 1 = 25
Shifting 1 to the Right Hand Side of the equation
4x = 25 - 1
Performing subtraction on Right Hand Side of the equation
4x = 24
Shifting 4 to the Right Hand Side of the equation as denominator
x = 24 ÷ 4
Performing division on Right Hand Side of the equation
x = 6
Thus, the solution is 6
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The correct question is - sqrt(4x+1)-5=0
Evaluate the expression 7+(-2)•3^2
Answer:first do the exponents thats equal to 9 then times -2 is -16+7 is -11
hope that helps
Step-by-step explanation:
Answer:
-11.
Step-by-step explanation:
7+(-2)•3^2
= 7 - 2*9
= 7 - 18
= -11.
The point k lies on the segment JL. Find the coordinates of k so that jk is 1/4 of JL L(19,10) J(-1,-2)
(4,5) i'm pretty sure I can't explain why but just go with it
Which equation has an extraneous solution?
Answer:
[tex] \sqrt[5]{x } = - 2 = - 35[/tex]
Each term of a sequence is 2 more than the previous term. if the third term is 8, find the first five terms of the sequence.
The first five terms of the sequence area s follows:
4, 6 , 8 , 10, 12
How to find the terms of a sequence?Each term of the sequence is 2 more than the previous term.
The third term is 8.
The sequence is an arithmetic sequence base on the difference.
Using arithmetic sequence formula,
aₙ = a + (n - 1)d
where
a = first termd = common differencen = number of termsTherefore, let's used the third term to find the first term.
8 = a + 2d
8 = a + 2(2)
8 = a + 4
a = 8 - 4
a = 4
Therefore, the first term of the sequence is 4.
Hence, the first five terms of the sequence area s follows:
4, 6 , 8 , 10, 12
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Find the difference.
3/4(3x+6)−1/4(5x−24)
Answer:
x+21/2.
Step-by-step explanation:
3/4(3x+6)-1/4(5x-24).
=9x/4-5x/4+9/2+6.
=x+21/2
Can a quadratic equation with real coefficients have exactly one imaginary root? Explain your answer.
A real coefficient quadratic equation cannot have one real root and one imaginary root.
What is a quadratic equation?A quadratic problem is a type of problem in mathematics that deals with a variable multiplied by itself — an operation known as squares. The area of a square is defined as its side length multiplied by itself in this language. The term "quadratic" is derived from the Latin word quadratum, which means "square." Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. Where x is an unknown variable and the numerical coefficients a, b, and c.A rational coefficient quadratic equation cannot have one real root and one imaginary root.Therefore, a real coefficient quadratic equation cannot have one real root and one imaginary root.
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Find the midpoint of the segment with the following endpoints (2,-9) (-4,-4)
Answer:
the answer will be (-1, -6.5)
Step-by-step explanation:
The midpoint formula is [tex](\frac{x^1 + x^2}{2} , \frac{y^1 + y^2}{2} )[/tex]
so you would do [tex](\frac{2 - 4)}{2} , \frac{-9-4}{2} )[/tex] , the only reason it is subtracting is that a positive and a negative make a negative so you might as well subtract, either way, if you insert the equation by doing 2 + (-4) you will get the same thing
then you would just do the math and get your answer
Hope this helps :)
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{-4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -4 +2}{2}~~~ ,~~~ \cfrac{ -4 -9}{2} \right) \implies \left(\cfrac{ -2 }{2}~~~ ,~~~ \cfrac{ -13 }{2} \right)\implies \left(-1~~,~~-6\frac{1}{2} \right)[/tex]
Use the Change of Base Formula to evaluate each expression.
log₇30
The evaluated value of [tex]log_{7}30[/tex] is 1.748
Change of base formula is used to change the base of the logarithm. It is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm.
According to the change of base formula:
[tex]log_{a}b = \frac{log_{x}b }{log_{x} a}[/tex]
where base x is considered base 10
According to the question, we have to find the value of [tex]log_{7} 30[/tex]
Thus applying change of base formula we get
[tex]log_{7} 30 = \frac{log_{10} 30}{log_{10} 7}[/tex]
calculating the value of log from the calculator we get,
[tex]log_{7} 30 = \frac{1.477}{0.845}[/tex]
[tex]log_{7} 30 = 1.748[/tex]
Thus evaluated value of [tex]log_{7}30[/tex] is 1.748
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12(?-21)=144 what is the answer
At the beginning of the day the stock market is 70 1/2 points and stays at this level for most of the day. At the end of the day, the stock market goes down 120 1/4 points from at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
Answer: 50 1/4
Step-by-step explanation:
Factor each expression.
x²-5 x+6
After solving, the factors of equation x²-5x+6 are:
(x-3) and (x-2)What is an equation, exactly?A mathematical statement made up of two representations joined by an equal sign is known as an equation.3x - 5 = 16 is an example of an equation.We obtain the value for the variable x as x = 7 after solving this equation.So,
Given the equation: x²-5x+6
Then,
x²-5x+6x²-x( + )+6x²-x(3+2)+6x²-3x-2x+6x(x-3)-2(x-3)Factors are: (x-3) and (x-2)
Therefore, after solving, the factors of equation x²-5x+6 are:
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If 3(x-2)= 2x+6 then x equals?
Answer:
x = 12
Step-by-step explanation:
First, distribute the 3 into the parentheses:
3(x-2) = 2x+6 ----> 3x-6 = 2x+6
Next, combine like terms by adding 6 to both sides of the equation:
3x-6 = 2x+6 ----> 3x = 2x+12
Then, subtract 2x from both sides:
3x = 2x+12 ----> 1x = 12
Finally, divide both sides by 1 to get x by itself:
x = 12
Confused on how to solve this
The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.
What is the limit?The value that approaches the output for the given input value. Limits are a very important tool in calculus.
The graph of the function is shown below.
The function is a piecewise function. The function is continuous between o to a, a to b, and b to till ∞.
The value of the function at b will be 1 which can be shown as,
[tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex]
The statement [tex]\begin{aligned} \lim_{x \rightarrow b} f(x)=1 \end{aligned}[/tex] will be true. Then the correct option is D.
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In AJKL and APQR, if JK PQ, LJ ZP, and ZK ZQ, then AJKL must be
congruent to APQR.
True or False
ΔJKL is congruent to ΔPQR. This statement is true.
Two figures are congruent if they have the same area and one figure is an exact image of the other.
Two triangles can be proven congruent by 4 axioms or rules.
SSS axiom. When all three corresponding sides of one triangle is equal to the sides of the other triangle then the triangles are congruent.SAS axiom . When two sides and the included angle of two triangles are equal, then both triangles are congruent.AAS axiom . When two angles and one side of a triangle is equal then the triangles are congruent.HL axiom . When the Hypotenuse and one leg of a right angled triangle is equal to the hypotenuse and leg of another triangle then the triangles are congruent.Given: in triangles ΔJKL and ΔPQR:
JK=PQ∠J=∠P∠K=∠QHence by AAS axiom of congruency triangles are congruent.
ΔJKL ≅ ΔPQR
The statement is true.
Disclaimer: The complete question is : In ΔJKL and ΔPQR, if JK= PQ, ∠J=∠P, and ∠K =∠Q, then ΔJKL must be congruent to ΔPQR.
True or False
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Can someone please help me with this one? I need it for my homework that I have to hand in tomorrow. Thank you!
The steps for constructing the bisector of an angle by using a ruler and compasses are as follows:
Step 1:
Take a compass and place its point on the angle's vertex Q.
Step 2:
Adjust the compass to the medium wide setting. The exact width is not important.
Step 3:
Without changing the compasses' width, draw an arc across each leg of the angle.
Step 4:
Now, place the compass on the point where one arc crosses a leg and draw the arc in the interior of the angle.
Step 5:
Without changing the compass setting repeat for the other leg so that the two arcs cross.
Step 6:
Now by using a ruler draw a line from the vertex to the point where the arcs cross.
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Step 1: Think of any number
Step 2: Double the number.
Step 3: Add-5
Step 4: Double your new number.
Step 5: Subtract 6
Step 6: Divide by 4/
Step 7: Subtract your original number
Did you get 1 ? use algebra to show why this works.
Answer:
Step 1: 20
Step 2: 40
Step 3: 45
Step 4: 90
Step 5: 84
Step 6: 21
Step 7: 1
I did get 1 by following the steps.
In a random sample of people, the mean commute time to work was minutes and the standard deviation was minutes. Assume the population is normally distributed and use a t-distribution to construct a % confidence interval for the population mean. What is the margin of error of ? interpret the results.
The margin of error is 3.083 min
Margin of Error: The margin of error is the range of error permitted around the sample statistic in order to estimate the population parameter. The margin of error indicates the size of the confidence interval. The breadth of the confidence interval increases with the margin of error.
Sample size, n=24
Sample mean, ¯x=31.5 min
Sample standard deviation, s=7.3 min
Confidence level, c=95%
=0.95
From the given information we can calculate the below-required quantities,
Significance level, α=1−c=1−0.95=0.05
Degrees of freedom, DOF=n−1
=24−1
=23
Now from the t-distribution table,
The value of t (α2, DOF) is,
t (0.025,23) = 2.069
Hence the margin of error will be,
MOE= t (α2, DOF) × s/√ n
=2.069×7.3/√24
=3.083 min
i. The upper limit of the confidence interval will be,
UL=¯x + MOE=31.5+3.083=34.583
The lower limit of the confidence interval will be,
LL=¯x−MOE
=31.5−3.083
=28.417
Hence, the 95% confidence interval is (28.417,34.583)
(28.417,34.583)
The answer is 28.417,34.583
ii. The required answer is MOE=3.083 min
ii. We have found the 95% confidence interval for the population mean to be (28.417,34.583). This means with 95 % confidence; it can be said that the population mean commute time is between the bounds of the confidence interval.
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The lengths of the four sides of a quadrilateral (in inches) are consecutive odd integers. if the perimeter is 120 inches, find the value of the longest of the four side lengths.
In a quadrilateral with a perimeter of 120 inches, the longest of the four sides has length equal to 33 inches.
A quadrilateral is a two-dimensional figure that has 4 sides and 4 vertices. The perimeter of any two-dimensional figure is the sum of all its sides.
If the lengths of the four sides of a quadrilateral (in inches) are consecutive odd integers, we can express each side as:
x = length of side 1(odd integer)
x + 2 = length of side 2
x + 4 = length of side 3
x + 6 = length of side 4
If the perimeter of the quadrilateral is 120 inches, then the sum of the four sides is equal to 120 inches.
x + (x + 2) + (x + 4) + (x + 6) = 120
Simplifying and solving for x.
4x + 12 = 120
4x = 108
x = 27
Substitute the value of x on the expression for the length of the 4th side(longest side).
longest side = x + 6 = 27 + 6
longest side = 33 inches
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A sketch of y = x² + 6x + 15 has been drawn.
Complete the sketch by entering the
corresponding values on the axes.
Answer:
Vertex=(-3,6) and Y intercept is 15/(0,15)
3. Between which two numbers is √74?
(A) 5 and 6
B) 6 and 7
7 and 8
C
D
8 and 9
1 1/2 ⋅ 2 1/3 (those are fractions help me please)
Answer:
3.5 in decimal form or 3 1/5
Step-by-step explanation:
Answer:
= - 1 1/6
Step-by-step explanation:
1 1/2 - 2 1/3
= 1 2/6 - 2 3/6
= 8/6 - 15/6
= - 7/6
= - 1 1/6
Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6:10. A multiplication table. Which statement explains whether Juliana is correct? She is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. She is correct because 6:10 can be written as 1:2 and there are an infinite number of ratios for 1:2. She is not correct because the multiplication table does not include multiples of 10. She is not correct because 6:10 is equivalent to 3:5 and there are only 9 ratios in the multiplication table that are equivalent to 3:5.
The statement that explains whether Juliana is correct is A. She is correct because she can multiply 6 and 10 by any number to form an equivalent ratio.
How to illustrate the information?From the information, it should be noted that
Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6:10.
It should be noted that she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio.
An example is (6 × 2)/(10 × 2) = 12/20
It should be noted that 6/10 is equivalent to 12/20.
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what value (s) of x will make x[tex]x^{2}[/tex] =9 true?
The values of x that will make x² = 9 are positive 3 and negative 3.
What is a quadratic equation?A quadratic equation is an algebraic equation that has highest degree of 2, therefore, it also has two roots or we can say it has two solutions.
We know sign distributions that negative distributed to a negative is positive and positive distributed to a positive also results in positive.
∴ 9 can be obtained by either multiplying (-3)(-3) or (3)(3).
So, the value of x that will make x² = 9 is
x = ± √9
x = ± 3.
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Help me please asap please
Answer:
the first one is D. {3/2}
second one is C. {-10}
Step-by-step explanation:
hope this helps
If I don't get an A in math my mom will hit me again
What is the product?
Enter your answer as a fraction, in simplified form, in the box.
-1/4 x -6/11
Answer:
[tex]\frac{3}{22}[/tex]
Step-by-step explanation:
To multiply fractions, just multiply the numerators (tops) times each other and the denominators (bottoms) times each other:
[tex]\frac{-1}{4}[/tex] x [tex]\frac{-6}{11}[/tex] = [tex]\frac{6}{44}[/tex]
Now all we have to do is to simplify. In this case, just find the largest number that goes evenly into the numerator and the denominator: it is 2. Divide numerator and denominator by 2 to get the final answer: [tex]\frac{3}{22}[/tex]
The points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU:UV:VWTU:UV:VW is equal to 1:5:2.1:5:2. If TW=32,TW=32, find UW.UW.
Answer:
The length of UV is 10 units.
Step-by-step explanation:
It is given that the points T, U, V and W all lie on the same line segment, in that order, such that the ratio of TU:UV:VW is equal to 1:5:2.
Now, we need to calculate UW if TW = 32.
So, TU : UV : VW = 2 : 5 : 5
=> TW = 24
From the above conditions it can be observed that;
=> Ratio of TU = 2
=> Ratio of UV = 5
=> Ratio of VW = 5
Firstly, we have to sum up the total ratio that is;
=> Total = Ratio of TU + Ratio of UV + Ratio of VW
=> Total = 2 + 5 + 5
=> Total = 12
Now, we need to calculate the length of UV from which we get;
=> UV = 5/12 * 24
=> UV = 10
Therefore; length of UV is 10 units.
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